Parallel Combination 🔀

Kai Raaste 🛣️

Parallel ka matlab hai: saare components ke dono sire ek hi jodi bindu se jude hain. Ab current ke paas kai raaste hain — wo bat kar sab mein jaata hai.

📌 Parallel ke do sunehre niyam (series ke bilkul ulte):

1️⃣ Voltage har branch par SAME hota hai
V = V₁ = V₂ = V₃

2️⃣ Current BAT jaata hai — sab branches jodkar kul current
I = I₁ + I₂ + I₃

Aur inse nikalta hai:
1/Rp = 1/R₁ + 1/R₂ + 1/R₃

5 Ω 10 Ω 30 Ω 2.4 A 1.2 A 0.4 A 12 V 12 V 12 V 4 A 4 A 12 V battery Har branch par POORA 12 V chahe R kuch bhi ho 2.4 + 1.2 + 0.4 = 4 A ✓
Parallel circuit: har branch par poora 12 V, par current resistance ke ULTE ratio (anupaat) mein bat'ta hai — sabse chhota resistor sabse zyada current leta hai.

🎯 Do zaroori patterns:

1️⃣ Sabse chhota resistor sabse zyada current leta hai. Kyunki V same hai aur I = V/R — toh chhota R matlab bada I. (Upar dekho: 5 Ω ne 2.4 A liya, 30 Ω ne sirf 0.4 A.)

2️⃣ Rp hamesha sabse CHHOTE resistor se bhi kam hota hai! Upar Rp = 3 Ω hai, jo 5, 10, 30 — teeno se kam hai.

Kyun? Kyunki ek aur raasta jodne ka matlab hai current ke liye aur jagah ban gayi — toh kul rukaawat ghat gayi. Parallel resistance ghataane ka tareeka hai.

🚪 Kai darwazon wali soch

Ek hall se bahar nikalne ka ek darwaza ho toh bheed lagti hai.

Ab teen darwaze khol do. Log bat jaayenge, aur bahar nikalna aasaan ho jaayega — yani kul rukaawat ghat gayi.

Aur agar ek darwaza sabse chauda ho? Sabse zyada log wahin se nikalenge — bilkul jaise sabse chhota resistor sabse zyada current leta hai.

Aur ek darwaza band ho jaaye? Baaki do se log phir bhi nikal sakte hain — yahi parallel ka sabse bada faayda hai.

🧮 Hal Kiye Hue Sawaal

📝 Sawaal 1 — Poora Parallel Circuit (upar wala diagram)

5 Ω, 10 Ω aur 30 Ω parallel mein 12 V se jude hain. Nikaalo: (a) kul resistance (b) har branch ka current (c) kul current.

Step 1 — kul resistance:
1/Rp = 1/5 + 1/10 + 1/30
LCM 30 lo: = 6/30 + 3/30 + 1/30 = 10/30
1/Rp = 1/3  →  Rp = 3 Ω

⚠️ Yahan sabse badi galti hoti hai: log 10/30 nikaal kar wahin ruk jaate hain aur R = 10/30 likh dete hain. ULTA (reciprocal) karna mat bhoolo!

Step 2 — har branch ka current (har par poora 12 V):
I₁ = 12/5 = 2.4 A
I₂ = 12/10 = 1.2 A
I₃ = 12/30 = 0.4 A

Step 3 — kul current (do tareeke, dono se same aana chahiye):
Tareeka A: I = I₁ + I₂ + I₃ = 2.4 + 1.2 + 0.4 = 4 A
Tareeka B: I = V/Rp = 12/3 = 4 A ✓

✅ Dono mel khaate hain — jawab sahi hai.

📝 Sawaal 2 — Do Barabar Resistor

Do 6 Ω ke resistor parallel mein. Kul resistance?

Hal: 1/R = 1/6 + 1/6 = 2/6 = 1/3 → R = 3 Ω

💡 Shortcut: do barabar R parallel mein = R/2. Aur n barabar R parallel mein = R/n.
Jaise chaar 8 Ω parallel mein = 8/4 = 2 Ω.

Aur sirf do alag resistor ke liye ye formula tez hai:
R = (R₁ × R₂) / (R₁ + R₂)

📝 Sawaal 3 — MIXED Circuit (Board Ka Favourite)

Ek 2 Ω ka resistor, do 4 Ω ke parallel jode ke saath series mein hai. Poora circuit 12 V se juda hai. Sab nikaalo.

Step 1 — pehle PARALLEL wala hissa hal karo (hamesha andar se bahar chalo):
4 Ω || 4 Ω = 4/2 = 2 Ω

Step 2 — ab wo 2 Ω, baaki 2 Ω ke SERIES mein hai:
Rtotal = 2 + 2 = 4 Ω

Step 3 — kul current:
I = V/R = 12/4 = 3 A

Step 4 — voltage kaise bata:
2 Ω wale par: V = 3 × 2 = 6 V
Parallel jode par: V = 3 × 2 = 6 V  (ya 12 − 6 = 6 V)

Step 5 — har 4 Ω mein current (dono par 6 V):
I = 6/4 = 1.5 A har ek mein

✅ Jaanch: 1.5 + 1.5 = 3 A = kul current ✓

📝 Practice — Khud Karo

(a) 2 Ω aur 3 Ω parallel mein. Rp = ?
Jawab: R = (2×3)/(2+3) = 6/5 = 1.2 Ω

(b) Teen 12 Ω ke resistor parallel mein. Rp = ?
Jawab: 12/3 = 4 Ω

(c) Upar wale (b) ko 6 V se jodo. Kul current?
Jawab: I = 6/4 = 1.5 A

🏠 Ghar Ki Wiring Parallel Mein Hi Kyun?

SeriesParallel
CurrentHar jagah sameBat jaata hai
VoltageBat jaata haiHar branch par same
Kul resistanceR₁ + R₂ + R₃ (badhta)1/R = 1/R₁ + 1/R₂ (ghatta)
Ek device kharab ho tohSab bandBaaki chalte rehte hain
Alag switchNahi ho saktaHo sakta hai
Har device ko poora voltageNahi miltaMilta hai
Kahan use hota haiFuse, switch, ammeterGhar ki poori wiring

🏠 Ghar mein parallel hi kyun — teen pakke kaaran:

1️⃣ Har upkaran ko poora 220 V milta hai. Bulb, TV, fridge — sabko wahi voltage chahiye jiske liye wo bane hain.

2️⃣ Har cheez ka apna switch. Aap pankha band karke bulb jala sakte ho.

3️⃣ Ek kharab, baaki theek. Ek bulb fuse hua toh poora ghar andhere mein nahi doobta.

⚠️ Par ek dhyaan dene wali baat: jitne zyada upkaran parallel mein jodoge, kul current utna badhta jaayega (kyunki Rp ghat raha hai). Isiliye har ghar mein fuse ya MCB lagta hai — jo current zyada hote hi line kaat deta hai.

🇮🇳 India Connection

Bharat ke gaon-dehat mein aksar ek hi socket se extension board par board jodkar kai cheezein chala li jaati hain. Ab aap physics se samajh sakte ho ki khatra kahan hai.

Har naya upkaran parallel mein judta hai. Har baar Rp ghatta hai, aur kul current badhta hai. Taar ki apni ek seema hoti hai — usse zyada current gaya toh H = I²Rt ke hisaab se wo garam hoga, phir uska plastic cover pighlega, aur phir short circuit aur aag.

Isiliye:
🔹 Ek socket par zyada bhaari upkaran (heater, geyser, iron) ek saath mat chalao
🔹 MCB ko kabhi bypass mat karo — wo aapki suraksha hai, rukaawat nahi
🔹 Agar taar garam lag raha hai, toh wo saaf chetavani hai

National Crime Records Bureau ke aankdon ke mutabik bharat mein aag lagne ke sabse bade kaarnon mein short circuit upar hai. Ye lesson sirf marks ke liye nahi hai.

🧠 Apne Aap Ko Test Karo

Q1. Parallel circuit mein voltage ka kya hota hai?
Q2. Do 6 Ω ke resistor parallel mein. Kul resistance?
Q3. Parallel mein kul resistance kaisa hota hai?
Q4. Parallel mein sabse ZYADA current kis branch mein bahega?
Q5. Ghar ki wiring parallel mein kyun hoti hai?
Q6. 2 Ω ek 4Ω||4Ω jode ke series mein hai, 12 V par. Kul current?
Q7. Parallel mein aur resistor jodne par kul resistance?

🧮 Numerical Trainer mein series, parallel aur mixed — teeno tarah ke sawaal hal karo!

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